4 citations · 4 across the 3 of their papers we have counts for
9 papers
Conservativity spectra and generalized Ignatiev model
Lev D. Beklemishev
We study a generalization of the notion of conservativity spectrum of an arithmetical theory to a language with transfinitely many truth definitions. We establish a correspondence…
Axiomatizing Origami planes
Lev Beklemishev, Anna Dmitrieva, Johann A. Makowsky
We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita--Justin axioms for the Origami constructions. We isolate the fragme…
Reflection algebras and conservation results for theories of iterated truth
Lev D. Beklemishev, Fedor N. Pakhomov
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theo…
Axiomatizing provable -provability
Evgeny Kolmakov, Lev Beklemishev
A formula is called \emph{-provable} in a formal arithmetical theory if is provable in together with all true arithmetical -sentences taken as additional…
A universal Kripke frame for the variable-free fragment of RC
Lev D. Beklemishev
This note characterizes a universal Kripke frame for the variable-free fragment of the reflection calculus with conservativity operators RC. The frame here is obtained fro…
Notes on a reduction property for GLP-algebras
L. D. Beklemishev
We consider some natural generalizations to the class of all GLP-algebras of the so-called reduction property for reflection algebras in arithmetic. An analogue of this property is…